A State-Space-Based Implicit Integration Algorithm for Differential-Algebraic Equations of Multibody Dynamics*

1997 ◽  
Vol 25 (3) ◽  
pp. 311-334 ◽  
Author(s):  
E. J. Haug ◽  
D. Negrut ◽  
M. lancu
Keyword(s):  
State Space ◽  
Multibody Dynamics ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Implicit Integration ◽  
Integration Algorithm ◽  
Implicit Integration Algorithm

State-Space Based Implicit Integration of the Differential-Algebraic Equations of Multibody Dynamics

1999 ◽  
Author(s):  
Dan Negrut ◽  
Edward J. Haug
Keyword(s):  
State Space ◽  
Mechanical System ◽  
Multibody Dynamics ◽  
Reference Frames ◽  
Differential Algebraic Equations ◽  
The State ◽  
Algebraic Equations ◽  
Implicit Integration ◽  
Euler Parameters ◽  
Generalized Coordinates

Abstract Three methods for the state-space based implicit integration of differential-algebraic equations of multibody dynamics are summarized and numerically compared. In the state-space approach, the time evolution of a mechanical system is characterized using a number of generalized coordinates equal with the number of degrees of freedom of the system. In this paper these independent generalized coordinates are a subset of the Cartesian position coordinates and orientation Euler parameters of body centroidal reference frames. Depending on the method, the independent generalized coordinates are implicitly integrated and dependent quantities (including Lagrange multipliers) are determined to satisfy constraint equations at position, velocity, and acceleration levels. Five computational algorithms based on the proposed methods are used to simulate the motion of a stiff 14-body vehicle model. Results show that the proposed methods deal effectively with challenges posed by stiff mechanical system simulation. A comparison with a state-space based explicit algorithm for the simulation of the same model indicates a speed-up of approximately two orders of magnitude.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

scholarly journals Time Integration and Assessment of a Model for Shape Memory Alloys Considering Multiaxial Nonproportional Loading Cases

2014 ◽  
Author(s):  
Wael Zaki ◽  
Xiaojun Gu ◽  
Claire Morin ◽  
Ziad Moumni ◽  
Weihong Zhang
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Time Integration ◽  
Implicit Integration ◽  
Proportional Loading ◽  
Simulation Data ◽  
Integration Algorithm ◽  
Implicit Integration Algorithm ◽  
User Material Subroutine ◽  
Martensite Reorientation

The paper presents a numerical implementation of the ZM model for shape memory alloys that fully accounts for non-proportional loading and its influence on martensite reorientation and phase transformation. Derivation of the time-discrete implicit integration algorithm is provided. The algorithm is used for finite element simulations using Abaqus, in which the model is implemented by means of a user material subroutine. The simulations are shown to agree with experimental and numerical simulation data taken from the literature.

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